All the credit cards listed are great credit cards to earn points and miles towards free travel. I will always list the best offer for you for all the credit cards I recommend.

• Chase Sapphire Preferred: 40,000 points for new applicants after $3,000 spend within the first 3 months; No foreign transaction fees; Earn 1 point for every $1 in purchases, and double points on all dinning, airfare, and hotels; Annual fee waived for the first year then $95/year. Card application link. Blog Post; Chase Sapphire Preferred vs. Chase Ink Bold post
• The New Chase Ink Bold: This new card just launched on 11/28. New applicants will receive 50,000 points after $5,000 spend within the first 3 months; Earn 1 point for every $1 in purchases, 2x points on gas and hotels, and 5x points on business spend (see post to see which categories apply). Annual fee waived for the first year then $95/year. Card Application link. Blog Post; Chase Sapphire Preferred vs. Chase Ink Bold post
• Chase Marriott Rewards Premier Visa Signature: 50,000 Marriott points for new applicants after first use of the card + 1 free award night (category 1-4); Free night (category 1-5) upon annual account renewal; Earn 1 Marriott point/$1 for every day spend; 2 Marriott points/$1 for dining, air, and rental car; 5 Marriott points/$1 on Marriott hotel spend; No foreign transaction fees; 15 nights towards status annually; Annual fee waived for the first year then $85/year. Card application link. Blog Post
• Chase Marriott Rewards Visa Signature: 30,000 Marriott points for new applicants after first use of the card + 2 free award night (category 1-4); Earn 1 Marriott point/$1 for every day spend; 2 Marriott points/$1 for dining, air, and rental car; 3 Marriott points/$1 on Marriott hotel spend; No foreign transaction fees; 10 nights towards status annually; Annual fee waived for the first year then $45/year. Card application link. Blog Post
• American Express Premier Rewards Gold Card: 15,000 points for new applicants after $1,000 spend within the first 3 months; Earn 3 points/$1 on airfare, 2 points/$1 on gas and groceries, and 1 point/$1 on everything else; Annual fee waived for the first year then $175/year. Card application link. Blog Post
• The NEW Business Gold Rewards Card from American Express Open: Currently there is no promotion for signing up for this credit card. Earn 3 points/$1 on airfare, 2 points/$1 on advertising, gas, and shipping, and 1 point/$1 on everything else; Annual fee waived for the first year then $175/year. (Let’s hope for another promotion soon similar to the previous 50,000 point promotion!) Card application link. Blog Post
• American Express Platinum: 25,000 Membership Rewards points bonus, redeemable for one domestic round-trip Coach-Class airline ticket, when you spend $2,000 during your first three months of Card membership; New GLOBAL Travel benefits: Priority Pass select airport club access, No Foreign Transaction Fees, Global Entry expedited U.S. immigration pass; Up to $200 in Airline Fee Credits annually to cover incidental charges on your airline of choice, including checked-baggage fees; Complimentary Companion Airfare with purchase of qualifying First- or Business-Class international ticket; 24/7 Platinum Card(R) Concierge service for assistance with reservations, travel, gifts, and more; FINE HOTELS & RESORTS Program: exclusive upgrades and amenities at over 700 boutique, resort, and luxury hotels worldwide. Card application link.
• Hyatt Rewards Credit Card: 2 Free nights at any Hyatt hotel after your first spend on the card; Diamond members get 2 free nights in a suite at any hotel (free night expires 1 year after opening the card and are not transferable); Earn 3 Hyatt Gold Passport points for every $1 spent at Hyatt properties; 1 Hyatt Gold Passport point for every $1 spent on all other purchases; No foreign transaction fees; Automatic Hyatt Gold Passport Platinum status. $75 annual fee (not waived the first year). Card application link. Blog Post
• Gold Delta SkyMiles Credit Card from American Express:
  • Limited time bonus: Business card – 55,000 miles with $10,000 in spend (25,000 points after your first purchase and 30,000 points after spending $10,000 in 6 months). Card application link.
  • Ongoing bonus: Personal card – 30,000 Delta miles after spending $500; First checked bag free for up to 9 passengers on the same itinerary; Zone 2 priority boarding on Delta flights; 20% In-Flight Savings on food and entertainment. Earn 1 miles/$1 spent on the card; Earn 2 miles/$1 spent on Delta; Annual fee waived for the first year then $95/year. Card application link. Blog Post
    
• United Airlines MileagePlus Explorer Card: 40,000 United miles for new applications (25,000 after first spend on the card and 10,000 additional miles adding an authorized and their first spend within two months of opening the account); Earn an additional 10,000 bonus miles/year when you spend $25,000+ each calendar year; Free first checked bag for you and your companion; Priority boarding; Earn 1 United mile/$1 spent on the card; Annual fee waived for the first year then $95/year. Card application link.
• American Express Starwood Preferred: 25,000 SPG points for new applicants after $5,000 spend within the first 6 months (10K after first spend and 20K after meeting minimum spend requirements); 2 stays/5 nights toward elite status yearly; Earn 1 SPG point for every $1 in purchases and double points on Starwood hotel spend; Annual fee waived for the first year then $65/year. Personal card application link; Business card application link. Blog Post
• Citi ThankYou Premier Card: 30,000 ThankYou points + free domestic companion ticket for new applicants after $2,000 in spend within the first 3 months; Earn 1.2 ThankYou points per $1 spent at grocery stores, gas stations, and drugstores, and 1 ThankYou point per $1 on all other purchases; Get a 33% bonus when redeeming on travel with their ThankYou Travel Center (30,000 = $399 in travel); No foreign transaction fees; Annual fee waived for the first year then $125/year. Card application link. Blog Post
  

Disclaimer: Some of the techniques to earn free travel involve applying for credit cards. The reader is solely responsible for the decisions he/she makes regarding their own credit.